detailed information: The input equation set is:
 | | | | 360000 | x | + | | 600 | y | + | | z | = | | 104000 | | (1) |
| | 1000000 | x | + | | 1000 | y | + | | z | = | | 160000 | | (2) |
| | 4000000 | x | + | | 2000 | y | + | | z | = | | 370000 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 25 Divide the two sides of equation (1) by 9, the equation can be obtained: | | 1000000 | x | + | | | 5000 3 | y | + | | | 25 9 | z | = | | | 2600000 9 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 | | | | 360000 | x | + | | 600 | y | + | | z | = | | 104000 | | (1) |
| - | 2000 3 | y | | - | 16 9 | z | = | | - | 1160000 9 | | (2) |
| | 4000000 | x | + | | 2000 | y | + | | z | = | | 370000 | | (3) |
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Multiply both sides of equation (1) by 100 Divide the two sides of equation (1) by 9, the equation can be obtained: | | 4000000 | x | + | | | 20000 3 | y | + | | | 100 9 | z | = | | | 10400000 9 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 | | | | 360000 | x | + | | 600 | y | + | | z | = | | 104000 | | (1) |
| - | 2000 3 | y | | - | 16 9 | z | = | | - | 1160000 9 | | (2) |
| - | 14000 3 | y | | - | 91 9 | z | = | | - | 7070000 9 | | (3) |
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Multiply both sides of equation (2) by 7, the equation can be obtained: | - | 14000 3 | y | | - | 112 9 | z | = | | - | 8120000 9 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 | | | | 360000 | x | + | | 600 | y | + | | z | = | | 104000 | | (1) |
| - | 2000 3 | y | | - | 16 9 | z | = | | - | 1160000 9 | | (2) |
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Multiply both sides of equation (3) by 16 Divide both sides of equation (3) by 21, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
 | | | | 360000 | x | + | | 600 | y | + | | z | = | | 104000 | | (1) |
| | |
Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 7, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
 | | | | 360000 | x | + | | 600 | y | = | | 54000 | | (1) |
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Multiply both sides of equation (2) by 9 Divide both sides of equation (2) by 10, get the equation:, then add the two sides of equation (9) to both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |